The coefficients \(1-{\cal W}_0/{\cal G}_0\) , \({\cal W}_1\) , \({\cal G}_1\) , \({\cal W}_2\) , and \({\cal G}_2\)  arising from different terms in the spatial covariant gravity induce distinct different effects on the GW propagations. In order to study the effects of the spatial covariant gravity on the GW propagation, we separately consider each term in (REF ) and () by setting others to be zero.
In this way, the four parameters \(\bar{\nu }\) , \(\bar{\mu }\) , \(\nu _A\)  and \(\mu _A\)  can be further parametrized in the following form [1]},
\(\mathcal {H} \bar{\nu } &=&\left[\alpha _{\bar{\nu }}(\tau )\left(k / a M_{\mathrm {LV}}\right)^{\beta _{\bar{\nu }}}\right]^{\prime }, \\\bar{\mu }&=&\alpha _{\bar{\mu }}(\tau )\left(k / a M_{\mathrm {LV}}\right)^{\beta _{\bar{\mu }}}, \\\mathcal {H} \nu _{\mathrm {A}} &=&\left[\rho _{\mathrm {A}} \alpha _{\nu }(\tau )\left(k / a M_{\mathrm {PV}}\right)^{\beta _{\nu }}\right]^{\prime }, \\\mu _{\mathrm {A}}&=&\rho _{\mathrm {A}} \alpha _{\mu }(\tau )\left(k / a M_{\mathrm {PV}}\right)^{\beta _{\mu }},\) 
